Paramodular forms coming from elliptic curves

There is a lifting from a non-CM elliptic curve E/Q to a paramodular form f of degree 2 and weight 3 given by the symmetric cube map. We find the level of f in terms of the coefficients of the Weierstrass equation of E. In order to compute the paramodular level, we use the available description of t...

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Bibliographic Details
Published in:Journal of number theory 2022-04, Vol.233, p.126-157
Main Author: Roy, Manami
Format: Article
Language:English
Subjects:
Elliptic curves
Local representations
Paramodular forms
Symmetric cube
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Summary:There is a lifting from a non-CM elliptic curve E/Q to a paramodular form f of degree 2 and weight 3 given by the symmetric cube map. We find the level of f in terms of the coefficients of the Weierstrass equation of E. In order to compute the paramodular level, we use the available description of the local representations of GL(2,Qp) attached to E for p≥5 and determine the local representation of GL(2,Q3) attached to E.
ISSN:0022-314X
1096-1658
DOI:10.1016/j.jnt.2021.06.007